Either I'm very tired and can't think, or this solution has a serious problem with negative signes everywhere.

A ratio of a/b=0.8 was picked just as an example for a gap.

Using r/b is just a better choice when it comes to interpreting results. When the ratio is 0.8, you're at the inner cylinder (since the smaller cylinder is defined as a/b=0.8), when it's 1, you're at the outer.